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X, Y and Z can do a piece of work in 6 hours. X and Y can do the same work in 8 hours and Z can the same work in 12 hours . In how many times will X and Z do the same work?

X, Y and Z can do a piece of work in 6 hours. X and Y can do the same work in 8 hours and Z can the same work in 12 hours . In how many times will X and Z do the same work? Correct Answer 8 hours

X + Y + Z can do 1/6 of job in one hour……1 X + Y can do 1/8 of job in one hour……2 Y + Z can do 1/12 of job in one hour……3 adding 2&3 we get X + Y + Y + Z = 1/8 + 1/12 X + Z + 2Y = 5/24…4 subtracting 1 from 4 we get Y = 5/24 – 1/6 = 1/24.substituting the value of Y in 4 we have X + Z + 2/24 = 5/24 X + Z = 5/24 – 2/24 = 3/24 = 1/8 hence X&Z will do 1/8 of job in one hour. So X & Z will do the work in 8 hours.

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